diff --git a/include/proto/session.h b/include/proto/session.h
index b9eb44771..049fc931c 100644
--- a/include/proto/session.h
+++ b/include/proto/session.h
@@ -47,7 +47,6 @@ int parse_track_counters(char **args, int *arg,
 			 int section_type, struct proxy *curpx,
 			 struct track_ctr_prm *prm,
 			 struct proxy *defpx, char **err);
-int conn_session_complete(struct connection *conn, int flag);
 
 /* Remove the refcount from the session to the tracked counters, and clear the
  * pointer to ensure this is only performed once. The caller is responsible for
diff --git a/include/types/connection.h b/include/types/connection.h
index ddc610e2b..60caa4dc8 100644
--- a/include/types/connection.h
+++ b/include/types/connection.h
@@ -86,7 +86,7 @@ enum {
 	/* below we have all handshake flags grouped into one */
 	CO_FL_HANDSHAKE     = CO_FL_SI_SEND_PROXY | CO_FL_SSL_WAIT_HS | CO_FL_ACCEPT_PROXY,
 
-	CO_FL_INIT_SESS     = 0x00000800,  /* initialize a session before using data */
+	CO_FL_INIT_DATA     = 0x00000800,  /* initialize the data layer before using it */
 
 	/* when any of these flags is set, polling is defined by socket-layer
 	 * operations, as opposed to data-layer. Transport is explicitly not
diff --git a/src/connection.c b/src/connection.c
index 007d3b1be..d1813f967 100644
--- a/src/connection.c
+++ b/src/connection.c
@@ -67,12 +67,12 @@ int conn_fd_handler(int fd)
 	if (!(conn->flags & CO_FL_POLL_SOCK))
 		__conn_sock_stop_both(conn);
 
-	/* Maybe we need to finish initializing an incoming session. The
-	 * function may fail and cause the connection to be destroyed, thus
+	/* The data layer might not be ready yet (eg: when using embryonic
+	 * sessions). If we're about to move data, we must initialize it first.
+	 * The function may fail and cause the connection to be destroyed, thus
 	 * we must not use it anymore and should immediately leave instead.
 	 */
-	if ((conn->flags & CO_FL_INIT_SESS) &&
-	    conn_session_complete(conn, CO_FL_INIT_SESS) < 0)
+	if ((conn->flags & CO_FL_INIT_DATA) && conn->data->init(conn) < 0)
 		return 0;
 
 	/* The data transfer starts here and stops on error and handshakes */
@@ -103,10 +103,12 @@ int conn_fd_handler(int fd)
 	}
 
  leave:
-	/* we may need to release the connection which is an embryonic session */
-	if ((conn->flags & (CO_FL_ERROR|CO_FL_INIT_SESS)) == (CO_FL_ERROR|CO_FL_INIT_SESS)) {
-		conn->flags |= CO_FL_ERROR;
-		conn_session_complete(conn, CO_FL_INIT_SESS);
+	/* we may need to release the connection which is an embryonic session
+	 * in case of failure. For this we use the init callback which will
+	 * detect the error and clean everything up.
+	 */
+	if ((conn->flags & (CO_FL_ERROR|CO_FL_INIT_DATA)) == (CO_FL_ERROR|CO_FL_INIT_DATA)) {
+		conn->data->init(conn);
 		return 0;
 	}
 
diff --git a/src/session.c b/src/session.c
index 62099213d..a32ec6b09 100644
--- a/src/session.c
+++ b/src/session.c
@@ -50,6 +50,7 @@
 struct pool_head *pool2_session;
 struct list sessions;
 
+static int conn_session_complete(struct connection *conn);
 static struct task *expire_mini_session(struct task *t);
 int session_complete(struct session *s);
 
@@ -58,7 +59,7 @@ struct data_cb sess_conn_cb = {
 	.recv = NULL,
 	.send = NULL,
 	.wake = NULL,
-	.init = NULL,
+	.init = conn_session_complete,
 };
 
 /* This function is called from the protocol layer accept() in order to
@@ -193,7 +194,7 @@ int session_accept(struct listener *l, int cfd, struct sockaddr_storage *addr)
 		t->process = expire_mini_session;
 		t->expire = tick_add_ifset(now_ms, p->timeout.client);
 		task_queue(t);
-		s->si[0].conn.flags |= CO_FL_INIT_SESS;
+		s->si[0].conn.flags |= CO_FL_INIT_DATA;
 		return 1;
 	}
 
@@ -266,12 +267,12 @@ static void kill_mini_session(struct session *s)
 /* Finish initializing a session from a connection, or kills it if the
  * connection shows and error. Returns <0 if the connection was killed.
  */
-int conn_session_complete(struct connection *conn, int flag)
+static int conn_session_complete(struct connection *conn)
 {
 	struct session *s = conn->owner;
 
 	if (!(conn->flags & CO_FL_ERROR) && (session_complete(s) > 0)) {
-		conn->flags &= ~flag;
+		conn->flags &= ~CO_FL_INIT_DATA;
 		return 0;
 	}